OFFSET
1,16
COMMENTS
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Additive with a(p^e) = floor(log_2(e)) = A000523(e).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} P(2^k) = 0.53331724743088069672..., where P(s) is the prime zeta function.
MATHEMATICA
f[p_, e_] := Floor[Log2[e]]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100]
PROG
(PARI) a(n) = vecsum(apply(exponent, factor(n)[, 2]));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Sep 28 2023
STATUS
approved